Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?
You have 27 small cubes, 3 each of nine colours. Use the small cubes to make a 3 by 3 by 3 cube so that each face of the bigger cube contains one of every colour.
How many solutions can you find to this sum? Each of the different letters stands for a different number.
In each of the squares in the grid, one of the letters P, Q, R and S must be entered in such a way that touching squares (whether connected by an edge or just a corner) do not contain the same letter. Some of the letters have alread been entered as shown.
What are the possibilities for the letter in the shaded square?
If you liked this problem, here is an NRICH task which challenges you to use similar mathematical ideas.
This problem is taken from the UKMT Mathematical Challenges.